You are a quant analyst reporting directly to a portfolio manager. Your manager requires you to generate a simple code to compute several statistics for the following potential portfolio;

Potential Portfolio

S&P 500 - long USD 10000

NASDAQ - long USD10000

Dow Jones Industrial Average - Long USD30000

United States Oil Fund - Short USD40000

United States Natural Gas Fund - Short USD10000

*The current position is given by

Current Portfolio

S&P 500 - long USD 15000

NASDAQ - long USD15000

Dow Jones Industrial Average - Long USD30000

United States Oil Fund - long USD20000

United States Natural Gas Fund - Long USD10000

In order to start your analysis, visit Yahoo Finance to download the weekly prices for the above securities /indices between 2 Jan 2009 to 31 Dec 2010

You are required to compute the portfolio statistics for the potential execution and current portfolio.

Current Portfolio

1. Prepare a MATLAB code that generates the following output; portfolio historical mean, portfolio volatility, skew and kurtosis, Sharpe Ratio and Max Drawdown. The required inputs are as follows; weekly return matrix R, weight vector w, a vector that allows user to include lower and upper bound on each position if he wishes to.

2. Compute a 95% confidence interval Value at Risk for the portfolio using a Cornish Fisher expansion.

3. Compute the annualized return and volatility of the portfolio. State clearly any underlying assumptions based on your approach taken.

4. Your manager would like you to optimize his current portfolio. Run an optimization of the function that you wrote in 1), (you may use the optimizer provided in MATLAB, but make sure you state clearly the steps and your chosen optimizer as your manager will need to know how to run the code in your absence). You are not supposed to use solver in excel. Report the optimized results.

Potential Portfolio

1. Using your codes prepared earlier perform the same computation in 1) for the potential portfolio. Explain in detail how you account for the negative positions in your portfolio.

2. Run the optimization again and report your findings.

3. Your manager for some reasons has specifically mentioned that he wants to short both the United States Oil Fund and United States Natural Gas Fund. Compute a reasonable vector for the lower bound and upper bound for the potential portfolio and use these vectors as a constraint for running an optimization of the potential portfolio. Report your findings.